<h2>Problem 113</h2>
<div style="color:#666;font-size:80%;">10 February 2006</div><br />
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<p>Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468.</p>
<p>Similarly if no digit is exceeded by the digit to its right it is called a decreasing number; for example, 66420.</p>
<p>We shall call a positive integer that is neither increasing nor decreasing a &quot;bouncy&quot; number; for example, 155349.</p>
<p>As <i>n</i> increases, the proportion of bouncy numbers below <i>n</i> increases such that there are only 12951 numbers below one-million that are not bouncy and only 277032 non-bouncy numbers below 10<img src="" style="display:none;" alt="^(" /><sup>10</sup><img src="" style="display:none;" alt=")" />.</p>
<p>How many numbers below a googol (10<img src="" style="display:none;" alt="^(" /><sup>100</sup><img src="" style="display:none;" alt=")" />) are not bouncy?</p>

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